Wire-cut electric discharge machine control system to compensate for wire flexure during machining

ABSTRACT

There is disclosed a method of controlling a wire-cut electric discharge machine to correct cutting errors due to flexing of a wire electrode caused by electric discharge. A processing unit processes data (x 1 , y 1 , r 1 , x 2 , y 2 ) on a corner shape which is given by a paper tape and data on an amount of flexing (D 0 ) upon rectilinear cutting for calculating a corrected radius of curvature r 1  &#39; of the corner, and determines the center Pc of an arc having the radius of curvature r 1  &#39; and contacting straight lines (l 1 , l 2 ) and points of contact Pt, Pt&#39; to move the wire electrode along a straight line P 1  Pt, an arc PtPt&#39;, and a straight line Pt&#39;P 3  to thereby correct the cutting error at the corner.

BACKGROUND OF THE INVENTION

The present invention relates to a method of controlling wire-cutelectric discharge machine to prevent cutting errors which would beproduced upon flexing of a wire electrode when a corner is cut during anelectric discharge cutting operation, and more particularly to a simplemethod of controlling a wire-cut electric discharge machine to carefullycut a corner.

Wire-cut electric discharge machines operate on the principle that avoltage is applied across a gap between a wire electrode and a workpieceto generate a spark discharge across the gap for cutting the workpiecewith the spark energy. The workpiece can be cut to a desired contour bymoving the workpiece with respect to the wire electrode based on cuttingcommand data.

More specifically, as schematically shown in FIG. 1 which shows a knownwire-cut electric discharge machine, a wire 1 is reeled out of a reelRL₁, extends between a lower guide 4 and an upper guide 4, and is woundaround a reel RL₂. A voltage is applied by a contact electrode (notshown) to the wire to generate a discharge between the wire 1 and theworkpiece 2 for cutting off the latter. The workpiece 2 is fastened to atable TB movable by motors MX, MY in directions X, Y, respectively.Thus, the workpiece 2 can be cut to a desired configuration by movingthe table TB in the directions X, Y. The upper guide 4 is attached to amoving mechanism MMC movable by motors MU, MV in the directions X, Y,respectively so that the upper guide 4 is movable in the directions X,Y.

The moving mechanism, the reels RL₁, RL₂, and the lower guide 4 aremounted on a column CM.

A numerical control unit NC serves to read the contents of a commandtape TP, and has a distributor circuit DS for distributing commands forrespective axes and drive circuits SVX, SVY, SVU, SVV for thecorresponding axes for energizing the motors MX, MY, MU, MV respectivelyfor the axes to move the table TB and the moving mechanism until theworkpiece 2 is cut to a desired shape.

FIG. 2 is illustrative of a cutting operation of such an electricdischarge cutting machine. When the wire electrode 1 moves in and alonga slot 3 in a given direction while cutting off the workpiece 2 withelectric discharge, a pressure is developed between the wire electrode 1and the workpiece due to the electric discharge to which pushes the wireelectrode 1 back in the direction of the arrows which is opposite to thedirection in which the electrode 1 moves along, as shown in thecross-sectional view of FIG. 3. The wire electrode 1 is therefore backedoff or flexes from the position of the wire guides 4, 4. The cuttingaccuracy is not affected to an appreciable extent by the amount of suchflexing as long as the wire electrode 1 cuts the workpiece 2 along arectilinear slot. However, the amount of flexing causes a seriousproblem when the wire electrode 1 cuts the workpiece to form a corner.Thus, as shown in FIG. 4 which is a plan view of a cut slot, a slot 3 iscomposed of a first rectilinear slot L1 and a second rectilinear slot L2extending perpendicularly to the first rectilinear slot L1, and definingsuch a combined slot 3 requiring a corner CN to be cut at the junctionbetween the first and second rectilinear slots L1, L2. To this end, theworkpiece 2 and the wire electrode 1 are caused to move relatively inone direction to form the first rectilinear slot L1, and thereafter thedirection of such relative movement needs to be a right angle asdirected by a cutting command to form the second rectilinear slot L2.The wire electrode 1 however has a tendency to be dragged inwardly ofthe corner CN due to the flexing of the wire electrode 1 at a positionin which the electric discharge takes place, with the result that thecontour of the slot 3 as it is cut is distorted considerably inwardlyand becomes blunt as shown by the dotted lines, a configuration which isdifferent from a commanded shape (shown by the solid lines).

FIG. 5 is a plan view of an arcuate corner CN' to be formed betweenfirst and second rectilinear slots L1, L2. In cutting such an arcuatecorner CN', the flexing of the wire electrode 1 due to the electricdischarge causes the corner CN' to be cut along a path shown by thedotted lines which is duller than a commanded shape as illustrated bythe solid lines.

It is known that the cutting errors at such arcuate and angular cornerscan be reduced by changing the path of cutting, the cutting powersupply, the speed of feed, and other factors. However, there are a greatmany combinations of such cutting conditions available, and thecustomary practice has been complex and impractical since no specificstandard has been established for controlling the cutting path, thefeeding speed, and the cutting power supply voltage.

Accordingly, it is an object of the present invention to provide asimple method of controlling a wire-cut electric discharge machine toimprove blunt corner shapes.

Another object of the present invention is to provide a method ofcontrolling a wire-cut electric discharge machine to correct the radiusof curvature of an arcuate corner into an optimum radius of curvature bytaking flexing of a wire electrode into consideration for cutting thearcuate corner with greatly increased accuracy.

SUMMARY OF THE INVENTION

With the present invention, data on an amount of flexing measured inadvance while cutting a workpiece along a straight line is stored, anddata on a commanded radius of curvature of a corner is corrected by thedata on the amount of flexing when cutting the corner. The workpiece ismoved with respect to a wire electrode along an arc determined by thecorrected radius of curvature for electric discharge cutting of theworkpiece with the wire electrode. Since the wire electrode follows thecommanded arc, the corner can be cut more accurately.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a wire-cut electric discharge machine;

FIG. 2 is a perspective view illustrative of the principle on which aworkpiece is cut by a wire due to electric discharge;

FIG. 3 is a cross-sectional view explanatory of flexing of the wireelectrode;

FIGS. 4 and 5 are plan views explanatory of problems with a conventionalelectric discharge cutting process;

FIGS. 6, 7, 8 and 9 are diagrams explanatory of arithmetic operationsfor determining amounts of flexing in tangential and radial directions;

FIG. 10 is a diagram illustrative of a process of measuring an amount offlexing while cutting along a straight line;

FIG. 11 is a diagram showing the way in which the radius of a correctedpath is determined for cutting a corner having a corner angle θ and aradius of curvature R₀ ;

FIG. 12 is a diagram explanatory of a cutting control method accordingto the present invention for cutting a corner; and

FIG. 13 is a block diagram of an arrangement for effecting the cuttingcontrol method of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will now be described in more detail withreference to the drawings.

While cutting a workpiece along a straight line, a wire electrode flexesin a direction (tangential direction) opposite to the direction in whichcutting progresses due to electric discharge pressure developed duringthe cutting operation. When the workpiece is cut along an arc or acorner, the wire electrode flexes not only in a tangential direction butalso inwardly of the arc or in a radial direction due to differentamounts cut outwardly and inwardly of a central path of movement of thewire electrode. For high-precision electric discharge cutting using acutting wire, the cutting control is required to take into considerationboth a force applied in a direction tangential to the path along whichthe workpiece is cut by the wire and a force imposed in a radialdirection. According to the present invention, these forces, namely,amounts of flexing in the tangential and radial directions are takeninto account for correcting the path of movement of the wire to preventthe shape of the corner from becoming blunt.

Processes of deriving equations for determining an amount of flexingD_(T) in the tangential direction and an amount of flexing D_(R) in theradial direction, and of correcting a path along which cutting iseffected using the amounts of flexing D_(T), D_(R) will successively bedescribed.

(A) Derivation of equations for determining the amounts of flexingD_(T), D_(R) in the tangential and radial directions:

It is assumed that a wire electrode 1 moves along an arcuate path havinga radius of curvature R to cut a workpiece 2 for forming a slot having awidth 2ε₀, as shown in FIG. 6.

When the wire electrode 1 moves through an angle θdt within a time dt, adifferentiated value dV of an amount of cutting with respect to time atthe position of an angle α in FIG. 6 for a workpiece having a unitthickness is given as follows: ##EQU1## Since a feeding speed F is:

    F=Rθ                                                 (1)

the following equation can be established: ##EQU2## On the assumptionthat electric discharge is produced on the front face of the wireelectrode 1, dV is integrated from α=0 to π and the following equationresults:

    V=2Fε.sub.0                                        (3)

With the wire electrode 1 at the position of the angle α of FIG. 6 beingunder pressure as shown in FIG. 7, the following presumptions 1 and 2are presented:

1. The pressure imposed by electric discharges on the wire electrodesurface is proportional to the frequency of the electric discharges,which is in turn proportional to an amount of cutting per unit time,namely, the speed of cutting; and

2. The pressure acts perpendicularly on the wire electrode surface.

Therefore, a force dP_(R) acting radially on the wire electrode 1 due tothe amount of cutting dV per unit time is given by: ##EQU3## Byintegrating the force dP_(R) from α=0 to π (the force dP_(R) is directedoutwardly), the following results: ##EQU4## where K is a proportionalityconstant. Although P_(R) in fact varies with the energy of a singleelectric discharge, such energies are assumed here to be equal (byrendering C, V in CV² /2 constant).

Likewise, a force dP_(T) acting on the wire electrode 1 in thetangential direction is given by: ##EQU5## By integrating the forcedP_(T) from α=0 to π, the following results: ##EQU6## As is apparentfrom the equations (3), (6), V and P_(T) are not dependent on the radiusof curvature R of the arc, and are regarded as an amount of cutting onrectilinear cutting and a force applied to the wire electrode 1.

The amount of flexing of the wire electrode 1 can approximately beexpressed in FIG. 8 as follows:

    D.sub.1 =PH/4T

    D.sub.2 =(L-H)P/2T

    D=D.sub.1 +D.sub.2 =K.sub.2 P                              (7)

where P is the pressure, H is the thickness of the workpiece 2, L is thevertical distance between guides 4, 4, and T is the tension to which thewire electrode is subjected.

The equation (7) indicates that the amount of flexing D is in proportionto the force acting on the wire electrode 1. With the presumption 1 inview, and assuming that an amount of flexing upon rectilinear cutting ata cutting speed F₀ is indicated by D₀, and amounts of flexing due to theforces P_(T), P_(R) respectively in the tangential and radial directionsare indicated by D_(T), D_(R), respectively, the following equations areestablished: ##EQU7## The equation (9) can be derived using theequations (5), (6) and (7).

From the equations (8), (9), the amounts of flexing D_(T), D_(R) in thetangential and radial directions can be determined if the amount offlexing D₀ upon rectilinear cutting at the cutting speed F₀, and thewidth 2ε₀ of the slot cut are measured. Proper cutting operation can beeffected at all times by correcting the path of movement of the wireelectrode by the intervals D_(T), D_(R). Therefore, for cutting theworkpiece along an arc as shown in FIG. 9, a path of movement should befollowed which is advanced D_(T), D_(R) respectively in the tangentialand radial directions. D_(R) =0 for cutting the workpiece along astraight line.

The arithmetic operation involving D_(T), D_(R) requires D₀, F, F₀, ε₀,R. The radius of curvature R is found from cutting data, and the slotwidth 2ε₀ is determined in advance by actually cutting the workpiece ona test basis and measuring its dimensions, the data being stored in annumerical control (NC) unit. The actual feed speed F is already known.Consequently, the NC unit must be supplied with data on the amount offlexing D₀ upon rectilinear cutting and data on the cutting speed F₀upon such rectilinear cutting for the arithmetic operation to determineD_(T), D_(R).

(B) Measurement of the amount of flexing D₀ upon rectilinear cutting:

FIG. 10 is illustrative of measurement of the amount of flexing D₀. Theamount of flexing D₀ upon rectilinear cutting can be measured asfollows:

During rectilinear cutting, electric discharge is temporarily stopped ata predetermined point of measurement (FIG. 10). With electric dischargethus stopped, the wire electrode no longer undergoes electric dischargepressure, whereupon the wire electrode 1 is pulled in the directiontoward the wire guides (see the dotted line in FIG. 10) until the wireelectrode 1 is held against the workpiece 2. When the wire electrode 1contacts the workpiece 2, a contact sensor device detects such acontact.

After the wire electrode 1 has been brought into contact with theworkpiece 2, the wire electrode 1 is backed off along the cutting pathwith respect to the workpiece 2. The wire electrode 1 may be moved backby displacing the table with the workpiece placed thereon in thedirection of the arrow A with respect to the wire electrode 1, or movingback the wire guides in the direction of the arrow B with respect to theworkpiece 2 where the electric discharge cutting machine has movablewire guides.

Continued withdrawal of the wire electrode causes the latter to be outof contact with the workpiece at a certain position. A distance F₀ 'which the wire electrode traverses in moving back from the position inwhich electric discharge is stopped to the position in which the wireelectrode starts to disengage from the workpiece is measured, and themeasured data is stored in a memory in the NC unit.

Then, a real amount of flexing D₀ is calculated according to thefollowing equation to thereby complete the measurement of the amount offlexing:

    D.sub.0 =g+D.sub.0 '                                       (10)

where g is the gap across which electric discharge takes place and canbe determined by:

    g=(2ε.sub.0 -φ)/2                              (11)

where 2ε₀ is the width of the slot and φ is the diameter of the wireelectrode, as shown in FIG. 10. Accordingly, by measuring the width 2ε₀of the slot and the diameter φ of the wire electrode and storing theirdata in advance, the amount of flexing of the wire electrode can bedetermined through effecting the arithmetic operations of the equations(10), (11). F₀ is stored in the NC unit as the cutting speed uponmeasurement of D₀ simultaneously with D₀.

(C) Correction of the path of the wire electrode:

After the amounts of flexing D_(T), D_(R) in the tangential and radialdirections have been determined, the path of the wire electrode iscorrected.

In order for the flexing wire electrode to trace a commanded path, thecommanded path should be corrected for the intervals D_(T), D_(R) asdescribed above. More specifically, when cutting the workpiece along thearc having a radius of curvature R as shown in FIG. 9, the commandedpath should be corrected so as to be an arc having a radius of curvature(R+ΔR), which is advanced D_(T), D_(R) respectively in the tangentialand radial directions. The relationship between the radius of curvatureR of the commanded path for arcuate cutting and the difference ΔRbetween the radius of curvature R and that of a corrected arcuate pathis as follows: ##EQU8## Therefore, by previously measuring and storingin a memory the amount of flexing D₀ upon rectilinear cutting at thecutting speed F₀, D_(T), D_(R) can be calculated by giving the cuttingcommand speed F, and ΔR can be calculated from the equation (12) forcorrecting the radius of curvature R of the corner.

Operation for cutting a corner having a corner angle and a radius ofcurvature R₀ as shown by the solid lines in FIG. 11 will now bedescribed.

Assuming that, in FIG. 11, a commanded path has a radius of curvature R₀and a corrected path (shown by the dot-and-dash line) has a radius ofcurvature R₁, the following results geometrically: ##EQU9## Therefore,##EQU10## By equalizing (L₀ -L₁) with ΔR in the equation (12), ##EQU11##From the equation (17), when θ=0, R₁ =R₀.

Based on the foregoing, an arcuate corner shape can be corrected in thefollowing steps with reference to FIG. 12.

(a) NC data which specifies a corner arc is punched in a paper tape. Thecorner arc is not indicated by an ordinary arc command, but directly bythe radius of curvature of the corner arc according to the following:##EQU12##

(b) The corner angle θ is determined from the commanded NC data, and thecorner angle θ, the radius of curvature r₁, the amount of flexing D_(T)in the tangential direction, and the amount of flexing D_(R) in theradial direction are used to calculate a radius of curvature r₁ ' ascorrected by the equation (17). The corner angle θ may be included inthe NC data in advance.

(c) The coordinates of the center of curvature Pc of an arc whichcontacts straight lines l₁, l₂ and has the radius of curvature r₁ ', andthe coordinates of points of contact Pt, Pt' are determined.

(d) The wire electrode is moved relatively to the workpiece along thestraight line PlPt'→the arc PtPt'→the straight line Pt'P₃.

FIG. 13 is a block diagram of an arrangement for effecting a cuttingcontrol method according to the present invention. Designated at 101 isa paper tape in which a cutting program (NC data) is punched, and 102 atape reader. The NC program contains numerical data (positional commanddata and path command data), M function instruction data, G functioninstruction data, and the like. A numerical control unit 103 comprises amicrocomputer including a processing unit 103a, a control program memory103b, a data memory 103c, a register 103d for storing the cutting speedF₀, the amount of flexing D₀ at the cutting speed, the slot width 2ε₀and the like, and a working memory 103e.

Designated at 104X, 104Y are pulse distributors, SVX, SVY servocircuits, MX, MY motors for respective axes.

When the processing unit 103a is supplied with corner shape data seeformula a (18) from the paper tape 101, the processing unit 103autilizes data stored in the register 103d to calculate an amount offlexing D_(T) in the tangential direction and an amount of flexing D_(R)in the radial direction from the equations (8), (9), and stores thesecalculated amounts into the working memory 103e. Then, the corner shapedata is used to determine a corner angle θ, and a corrected radius ofcurvature r₁ ' is calculated from the equation (17) using the cornerangle θ, the radius of curvature r of the corner, the amount of flexingD_(T) in the tangential direction, and the amount of flexing D_(R) inthe radial direction. Thereafter, the coordinates of the center ofcurvature Pc of an arc having the radius of curvature r₁ ' andcontacting the straight lines l₁, l₂ (FIG. 12), and the coordinates ofthe points of contact Pt, Pt' are determined, the coordinates of thepoints Pc, Pt, Pt' being stored into the working memory. Increments ΔX,ΔY from a point P₁ to the contact point Pt are determined and suppliedto the following pulse distributors 104X, 104Y. The pulse distributors104X, 104Y effect an arithmetic operation for pulse distribution basedon the increments ΔX, ΔY to supply distributed pulses Xp, Yp to theservo circuits SVX, SVY to thereby drive the motors MX, MY. Thus, theworkpiece is moved with respect to the wire electrode from the point P₁to the contact point Pt. When the pulse distribution up to the contactpoint Pt is finished, the processing unit 103a generates data requiredfor pulse distribution for the arc PtPt' using the coordinates of thepoints Pt, Pc, Pt', and delivers the generated data to the pulsedistributors 104X, 104Y to move the workpiece along the arc PtPt'.Finally, increments ΔX', ΔY' from the contact point Pt' to the point P₁are determined, and the workpiece is moved from the contact point Pt' tothe point P₁ by pulse distribution based on the increments ΔX', ΔY',whereupon cutting of the corner shape is completed.

The present invention is highly advantageous in that electric dischargecutting can be effected along an accurate cutting path by correcting theradius of curvature of a corner to be cut irrespective of flexing of awire electrode, and the radius of curvature of the corner canautomatically be corrected simply by giving data on the radius ofcurvature and determining flexing of the wire electrode upon rectilinearcutting.

What is claimed is:
 1. A method of controlling a wire-cut electricdischarge machine to apply a voltage between a wire electrode and aworkpiece of relatively uniform thickness for cutting a corner of theworkpiece with electric discharge energy while the wire electrode andthe workpiece are being moved relative to each other based on cuttingcommand data including commanded radius data to thereby cut theworkpiece to a predetermined shape, said method comprising the stepsof:(a) storing data Do on an amount of flexing of the wire electrode asmeasured upon rectilinear cutting before the actual corner machiningoperation; (b) calculating an amount of flexing D_(T) of the wireelectrode in a tangential direction to the path along which theworkpiece is cut by the wire and an amount of flexing D_(R) of the wireelectrode in a radial direction to the path along which the workpiece iscut by the wire on the base of said data Do; (c) calculating a correctedradius of curvature R₁ of a corner to be cut on the basis of said amountof flexing D_(T) and said amount of flexing D_(R) ; and (d) moving thewire electrode and workpiece with respect to each other along an arcdetermined by the corrected radius of curvature R₁ of the corner forelectric discharge cutting of the workpiece.
 2. A method according toclaim 1, wherein the amount of flexing D_(T) and the amount of flexingD_(R) are calculated from said D₀, and a corrected radius of curavatureR₁ is determined using said amounts D_(T), D_(R), a corner angle θ, aradius of curvature R to cut the workpiece, and a radius of curvature Roof the corner through the arithmetic operation: ##EQU13##
 3. A methodaccording to claim 2, wherein said amount of flexing D_(T) in thetangential direction and said amount of flexing D_(R) in the radialdirection at a cutting speed F are determined by the followingarithmetic operations: ##EQU14## where F₀ is the cutting speed at whichthe amount of flexing D₀ is generated, R₀ is the radius of curvature ofthe corner, and 2ε₀ is the width of a slot to be cut.